document.write( "Question 1143530: solve: (x+iy)^5 + (x-iy)^5 = -8 \n" ); document.write( "

Algebra.Com's Answer #764368 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "There is one equation in two variables; it can't be SOLVED. You can only expand the binomials and SIMPLIFY the expression on the left.

\n" ); document.write( "Use the 5th row of Pascal's Triangle and the binomial theorem to expand both terms.

\r\n" );
document.write( "   (x+iy)^5 = x^5 + 5x^4y(i)    + 10 x^3y^2(i^2)    + 10 x^2y^3(i^3)    + 5xy^4(i^4)    + y^5(i^5)\r\n" );
document.write( " + (x-iy)^5 = x^5 + 5x^4(-y)(i) + 10 x^3(-y)^2(i^2) + 10 x^2(-y)^3(i^3) + 5x(-y)^4(i^4) + (-y)^5(i^5)\r\n" );
document.write( "--------------------------------------------------------------------------------------------------------------\r\n" );
document.write( "             2x^5               + 20x^3y^2                              + 10xy^4\r\n" );
document.write( "

\n" ); document.write( "It makes no sense to say to set that expression equal to -8 and ask to solve the equation.... \n" ); document.write( "

\n" );